The prob. of Lotto.

Q. To win the California Super Lotto Jackpot, contestants must match 5 numbers from 1 to 47 plus the Mega number, 1 to 27. What
are the number of possible number combination in this game? What is the probability that number picked at random will match a)
3 of 5 lotto numbers and the Mega number? B) 3 of 5 lotto numbers but NOT the Mega number?

The first question is easy to me. The answer is 47C5 x 27C1. Right?
However, my stuck questions are the 2nd and 3rd. My answer to the 2nd is 47C3 x 27C1 and to the 3rd is 47C3. Right? Your check is needed. Please help me.